Question

A certain principal amounts Rs. 500 in 3 years and Rs. 540 in 5 years. Find the rate of interest per annum.​

Answer 1

Answer:

20 rs per annum

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Step-by-step explanation:

Let the principal amount be =x

X= 500 in 3 years

X=540 in 5 years

That means it increased by 40.rs in 2 year.

So per annum it increases by 40÷2=20

X= 440

As it increases by 20 rs per annum

Therefore 20 rs is the rate of interest rate per annum

Answer 2

Given:

$P_1=500\\P_2=540\\T_1=3 \ year\\T_2=5 \ year$

To find:

rate of interest=?

Solution:

S.I. for 2years = Rs. (540-500)

=40 Rs.

S.I. for 1 year:

= $(40 \times \frac{1}{2}\times 1)$

=  20 Rs.

interest amount in 3 years =60

interest amount in 5 years =100

Principal amount (P) =Total Sum(Maturity Amount) -  interest amount

$\to P_1 = 500-60\\\\\to P_1= 440\\\\\to P_2=540-100\\\\\to P_2=440$  

$\bold{S.I=\frac{P\times R\times T}{100}}$

$\to R=\frac{S.I\times 100}{P_1\times T}\\\\\to R=\frac{500 \times 100}{440\times 1}\\\\\to R=\frac{500 \times 10}{44\times 1}\\\\\to R=\frac{5000}{44}\\\\\to R=113.63\%$